7. Let (V, ⟨⋅, ⋅⟩) be an inner product space and let R, S be subsets of V .(a) Prove that S ∩ S⊥ = 0

To prove that S ∩ S⊥ = {0}, we need to show that the only vector that is both in S and S⊥ is the zero vector.

Step 1: Assume that there is a vector v that is in both S and S⊥. This means that v is orthogonal to every vector in S, including itself.

Step 2: The definition of orthogonality in an inne Knowee AI is a powerful AI-powered study tool designed to help you to solve study problem.